Geodesic
Atomicity And Nilpotence
Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 365-382

Voir la notice de l'article provenant de la source Cambridge University Press

There is a body of results for lattices known as “Decomposition Theory” which is aimed at proving certain existence and uniqueness theorems concerning irredundant representations of elements of a compactly generated lattice. The motivation for these results is certainly the quest for sufficient conditions on congruence lattices to insure irredundant subdirect representations of algebras. These theorems usually include some kind of modularity or distribut i v e hypothesis (for uniqueness) and some atomicity hypothesis (for existence); the precise details can be found in [3]. The atomicity condition is usually the hypothesis that the lattice in question is strongly atomic or at least atomic. Now, it is well-known that every algebra has a weakly atomic congruence lattice. 
Kearnes, Keith A. Atomicity And Nilpotence. Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 365-382. doi: 10.4153/CJM-1990-020-1
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[1] 1. Burris, S. and Sankappanavar, H.P., A course in universal algebra, Graduate Texts in Mathematics 78 (Springer-Verlag, New York, 1981). Google Scholar

[2] 2. Camillo, V. and Fuller, K., A note on Loewy rings and chain conditions on primitive ideals, in Module theory, Lecture Notes in Mathematics 700 (Springer-Verlag, New York, 1979), 75–86. Google Scholar

[3] 3. Crawley, P. and Dilworth, R.P., Algebraic theory of lattices (Prentice-Hall, Engelwood Cliffs, N.J., 1973). Google Scholar

[4] 4. Freese, R. and McKenzie, R., Commutator theory for congruence modular varieties, LMS Lecture Note Series 125, Cambridge (1987). Google Scholar

[5] 5. Hall, M. Jr., Theory of groups, 2nd ed. (Chelsea Publishing Co., New York, 1976). Google Scholar

[6] 6. McKenzie, R., Finite equational bases for congruence modular varieties, Algebra Universalis 24, (1987), 224–250. Google Scholar

[7] 7. Vaughan-Lee, M.R., Nilpotence in permutable varieties, in Universal algebra and lattice theory, Lecture Notes in Mathematics, 1004 (Springer-Verlag, New York, 1983), 293–308. Google Scholar

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